Ovechkin's game-winner came after he skated down the right side of the ice and faked his way past a defender. He got off a shot that bounced along the ice and found its way through the legs of Senators goalie Pascal Leclaire.
It was the Russian superstar's third goal in two games for the Caps.
Eric Fehr contributed goal and an assist. Alexander Semin chipped in with a goal and Michal Neuvirth stopped 29-of-31 shots to earn the victory for Washington.
Ryan Shannon and Jarkko Ruutu found the net in the Senators' third straight loss to start the season.
Leclaire turned aside 23 shots for Ottawa.
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